what would happen if mass were continually added to a 2 msun neutron star?

End points of stellar evolution

Starting Mass	Outcome	Last Mass	Terminal Size	Density
> 20 M_Sun	Blackness Hole	whatever	two.95 (M/M_Sun) km	N/A
8 < M < twenty M_Sun	Neutron star	< 3-4 M_Sun	10 &minus 20 km ( &darr M )	10¹⁸ kg/chiliad³
0.4 < K < 8 M_Sun	White Dwarfs (Carbon)	< 1.4 M_Sun	7000 km ( &darr M )	10⁹ kg/mⁱⁱⁱ
0.08 < M < 0.4 M_Sun	White Dwarfs (Helium)	0.08 < M < 0.4 Thou_Sun	14000 km ( &darr Yard )
Thousand < 0.08 M_Sun	Brown Dwarfs	M < 0.08 Chiliad_Sun	10^v km

Nascence of a Neutron Star

The death of a loftier-mass star (such as Betelgeuse) will leave behind a neutron star.
Initially, the neutron star volition be very hot, most 10^eleven One thousand.
It will glow mainly in the X-ray part of the spectrum.
Over its offset few hundred years of life, the neutron star's surface cools down to 10⁶ G and continues to glow in the x-ray.
Immature neutron stars are found in supernova remnants.

X-ray Prototype of the Puppis A Supernova Remnant

The small point-source is a neutron star.

The neutron star is non at the centre since information technology was violently kicked by the supernova explosion.

The neutron star moves with a velocity of g km/south.

The Crab Nebula

In the twelvemonth 1054 A.D. the Chinese Courtroom astronomer/astrologer Yang Wei-Te noticed a bright new star which suddenly appeared in the constellation Taurus.
At its brightest (Supernovae explosion), information technology was almost as bright as Venus
It was visible during the daytime for 23 days and then continued to exist visible to the naked centre at night for another 653 days.
In the year 1731 John Bevis observed a "fuzzy" white nebula at the same location as the new star.
Charles Messier observed the nebula in 1758. Messier was interested in finding comets and wanted to make a catalogue of "slow" non-comet fuzzy objects. This nebula became the start object in his catalogue, M1.
The fuzzy nebula is called the Crab Nebula or M1 today.

Truthful Colour Photo of the Crab Nebula

Blood-red = Hydrogen Balmer transition respective to ionized hydrogen recombining with electrons.
Blue = Synchrotron emission as electrons spiral effectually magnetic field lines.
photo made past astrophotographer David Malin

The total power output by the Crab Nebula is 10⁵ L_Sun
This is incredible, since it is most 1000 years later the supernova explosion.

The neutron star inside this nebula rotates once every 33 ms (or about 30 times a second).
Nosotros see a bright spot on the neutron star, so the star appears to flash once every rotation menses.
Nosotros now say this neutron star is a pulsar .

The Nearest Neutron Star

Nearest to Earth neutron star is in Corona Australis - 200 lite-years away.
This is a more detailed photograph (in visible light) of RX J1856.5-3754 made with the ground-based telescope "Kueyen" in Chile.

Kueyen is an 8 thou telescope which is office of 4 telescope assortment whose lite will be combined to make an equivalent sixteen m telescope.

This picture shows a faint red deject around the neutron star.

The red light is Hydrogen Balmer Blastoff emission.

Photons emitted by the hot neutron star (T = 700,000 K) are exciting the Hydrogen surrounding the neutron star.

Structure of a Neutron Star

A neutron star balances gravity with neutron degeneracy pressure.

The neutrons separated past a distance = d have a velocity given by the Heisenberg Uncertainty principle:
v = h/(ii &pi m d)
where m is the mass of the neutron and h is Planck'due south constant.

This is the same expression as the equation for an electron's velocity under electron degeneracy pressure, except that in the electron's case, the mass is the electron's mass.

The neutron is about 2000 times more than massive than an electron, m_n = 1800 thousand_east.

In social club for the degenerate neutrons to have the same velocity as the degenerate electrons the neutrons must exist 1800 times closer to each other than the electrons in a white dwarf star.

A neutron star with the aforementioned mass as a white dwarf has a radius about 1000 times smaller than a white dwarf.

Typical radius for a neutron star is 10 km.

Average density &rho of a 10 km star with a mass of 2 M_Sun is
&rho = 4 ten 10³⁰ kg ten three/( 4 &pi x 10¹² thousand³) = 10¹⁸ kg/m ³

This is one billion times more dense than a white dwarf.

Uncertainty about a neutron star'southward structure

It is not known what really lies at the core of a neutron star.

Exotic particles such equally pions or unbound quarks might lie in the core.

Each theory near the dense core provides a correction to neutron degeneracy pressure.

Since the detailed nature of the cadre is unknown, the forces opposing gravity are not known exactly and the sizes of neutron stars are not known exactly.

For instance, ii dissimilar, but reasonable theories of neutron stars predict two different sizes for a neutron star with 1.4 M_Sun. One prediction is for a radius of 10 km, the other predicts a radius of 20 km.

If you lot could accurately mensurate the radius of a neutron star and measure its mass, you lot could dominion out certain theories describing dense nuclear matter.

However, very difficult to measure out the radius of a star this tiny.

Maximum Mass of a Neutron Star

White dwarfs tin can't have a mass larger than 1.four Thousand_Sun (the Chandrasekhar limit) since their electrons tin't motion faster than lite.
Neutron stars have a similar blazon of limit.
Each theory of nuclear thing predicts a different maximum mass for neutron stars.
Maximum masses range from 1.five to 4 Thou_Sun.
If you measure a neutron star's mass, you tin dominion out theories with predicted maxima below your measured mass.
The maximum mass is of import for identifying black holes.
A black hole in a binary star arrangement has properties very similar to a neutron star, so they are hard to place.
Suppose that you lot detect a mysterious object which is probably either a neutron star or a black pigsty. If you measure out the mass and find out that information technology is above the maximum mass limit for neutron stars, and then it must be a black hole.

The Discovery of the Offset Neutron Star

Neutron stars were first theoretically predicted by Walter Baade and Fritz Zwicky in the 1930'southward.

The properties seemed so bizarre that nobody took the prediction very seriously.

In 1967 Jocelyn Bell was doing observations using a new radio telescope for her Ph.D. thesis.

She discovered a radio indicate at one particular location which pulsed on and off with a menstruation of one.337 s.

She and her supervisor, Antony Hewish, get-go came to the decision that this was a bespeak from an alien civilisation and chosen the point LGM = Little Green Men

Afterward finding a 2nd like object at another location they realised these must be existent astronomical bodies.

They came to the conclusion that they must be pulsars.

In 1974 Hewish was awarded the Nobel prize in physics for the discovery of pulsars.

Now over 1000 neutron stars accept been discovered. Among them 200 very fast millisecond pulsars

Pulses for some pulsars have been seen in gamma-rays, x-rays, visible light, infrared, and radio

Maximum Spin Charge per unit of a Neutron Star

A rotating object tin't spin as well fast, or it volition exist torn apart by the "centrifugal strength".
The spin period = P is the time for a star to brand i rotation.
Equate gravitational force at the surface and centrifugal force GM/R² = &omega² R
to notice the maximum possible athwart velocity &omega and, thus, the minimum possible period P=ii &pi/&omega
The minimum spin period for an object with mass K and radius R approximately:

P_min = 2 &pi (R³/(GM))^ane/ii = ( 3 &pi / (Thou &rho)) ^1/2

The minimum spin menstruum for some astronomical objects is:

Object	P_min	Actual spin period	Actual catamenia / Minimum menstruum
Earth	5100 s = 1.iv hours	1 24-hour interval	17 x slower
Jupiter	10,000 south = 2.viii hours	x hours	4 10 slower
Sunday	x,000 s = two.8 hours	25 days	216 x slower
White Dwarf	about nine s
Neutron Star	0.v ms	Fastest is 1.4 ms	iii ten slower

Neutron stars can spin very rapidly because they are tiny and very dense! One tin can immediately deduce that the density must exist high. Even if P=1 s, &rho > 3 &pi/(One thousand P²) = 10¹¹ kg/m³. Could information technology be a white dwarf ? Perhaps, but Crab pulsar with 33 millisecond period can't be for sure !

In 1982 the most rapidly rotating neutron star had P = ane.half dozen ms (Spin frequency = 600 Hz).
In 2005 Jason Hessels (BSc. from U of A) discovered a neutron star with P = 1.4 ms (Spin frequency = 715 Hz).

Formation of a Rapidly Rotating, Magnetized Neutron Star

Same principles that nosotros considered during collapse of protostars

A neutron star is formed from the collapse of a much larger star.

Angular momentum is conserved during a collapse, and then the spin rate increases.

Spin period is proportional to (radius)^two

For example: The Sun is about 5 orders of magnitude larger than a typical neutron star.
- If we collapse the Sun downwardly to the size of a neutron star, it will have a spin period 10^-10 times smaller than the Sun.
- ie. it would spin with a period of 0.two ms
- Information technology is very easy to create a neutron star which spins with a period near a millisecond.

Similarly, magnetic flux is conserved during a collapse so that the magnetic field force is proportional to 1/(radius)²
- If the Sun collapses down to the size of a neutron star, its magnetic field volition exist 10 billion times stronger.

Typical magnetic fields on neutron stars are 10¹² times stronger than the Dominicus's magnetic field.

A minor number of neutron stars have magnetic fields 10¹⁴ times the Sun's magnetic field.

These ultra-stiff magnetic field neutron stars are chosen magnetars.

See Feb. 2003 Scientific American for a great commodity on magnetars

Even small initial rotation and magnetic field of neutron stars is highly amplified during the collapse

The Pulsar Mechanism

The stiff magnetic field of a neutron star creates a magnetosphere effectually the neutron star.

The magnetic poles are not usually aligned with the spin axis.

Inside the neutron star, the electromagnetic forces rip off the electrons on the surface and the electrons get trapped by the magnetic field.

The electrons become funnelled forth lines of force pointing out of the due north and south magnetic poles.

The electrons are highly accelerated and they radiate synchrotron radiation which is beamed outwards in the directions of the poles.

The spin of the star causes the beam of radiation to intersect our line of sight once a spin period.

Nosotros see a pulse of low-cal which turns on and off with a regular period. (Light-house mechanism)

Nosotros call this type of neutron star a pulsar.

A magnet which spins nearly an axis different from its symmetry axis emits radiation which causes it to lose energy.

This loss of free energy causes the magnet'due south spin to slow down.

The neutron star must wearisome down, which means that its spin period must increase slowly with fourth dimension.

Pulsar Recycling

Neutron stars are born chop-chop rotating only slow down due to the magnetic drain of their energy.
This would propose that over fourth dimension all old pulsars should spin slowly.
Notwithstanding, if a neutron star is in a binary system things alter.
Matter tin flow from the companion to the neutron star through an accretion deejay.
Equally matter from the deejay falls onto the neutron star, it adds mass and angular momentum (or spin) to the neutron star.
This slowly causes the neutron star to spin faster.
This process is called recycling.
The accession disk is very hot and typically radiates x-rays.
When Hydrogen and Helium are dumped onto the surface, small nuclear explosions occur causing bursts of 10-rays.
When the explosion takes place on simply a small office of the star, we see the explosion only once every spin menstruum, so the burst seems to flicker.
Flickering X-ray Bursting neutron stars have been observed which propose that they spin with periods in the range of three ms to ane.6 ms.

Lite Curve for an X-ray Burst

The large graph shows how effulgence varies with time during an X-ray Outburst.

If the time centrality was expanded, y'all would be able to encounter a periodic wave with a frequency of 530Hz.

The inset shows a "Fourier Spectrum" which shows the ascendant repetition frequency in the data.

The Crab Nebula in Radio, Optical and X-rays

This shows a recent composite pic of the innermost region of the Crab Nebula (fabricated by combining images from the Chandra X-ray Telescope, Hubble Space telescope and NRAO radio telescopes).

Cerise = Radio emission

Green = Visible emission

Blueish = 10-ray emission

The Crab Pulsar is hidden in the heart of the rotating disk. The disk is caused by a current of air originating from the pulsar.

The pulsar moves in the same management every bit its spin axis! Suggests that the supernova gave a peculiar type of "kicking" to the neutron star during its nascence.

Adjacent lecture: Black Holes

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Source: https://sites.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect19/lecture19.html